This coterminal angle calculator converts an angle in degrees or radians into two positive co-terminal angles and two negative co-terminal angles.

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## Coterminal Angle Formula

The following formulas are used to calculate coterminal angles.

Positive Coterminal Angle = Angle + 360

Negative Coterminal Angle = Angle -360

To calculate the coterminal angle, add and/or subtract 360 degrees from the current angle.

The formulas above would only yield one of each co-terminal angle. In reality, there is an infinite number of co-terminal angles. The definition is simply an angle that ends at the same point as another angle on a coordinate plane. Since the coordinate circle has a total rotation of 360 degrees, adding or subtracting that to the angle yields a result, as does the coterminal angle calculator above.

To calculate a coterminal angle between 0 and 2π, in terms of pi, you must add or subtract 2π from the fractional pi value given. For example:

Find the coterminal angle of 11π/3:

Since 11π/3 > 2π, subtract 2π from the given angle. If the given angle was less negative, you would add 2π.

11π/3 - 2π/1 = 11π/3 - 6π/3 = **5π/3**.

## Coterminal Angle Definition

A coterminal angle is an angle that ends at the same geometric point on the coordinate plane as another angle.

## Common Coterminal Angle Values

The following list outlines the coterminal angles of the most commonly calculated angles.

## How to calculate a coterminal angle

Let's take a look at an example of how you might calculate the coterminal angle.

- Let's assume you are given an angle in radians. For this example, the angle is 2.5 radians.
- First, you must convert the radians to degrees. 1 radian is equal to 57.29 degrees so 2.5*57.28=114.59 degrees
- Last, we need to add 360 degrees to that angle to find an angle that is coterminal with the original angle, so 114.59+360 = 475.59 degrees.
- Check the answer using the calculator above.

## FAQ

**What is a coterminal angle?**

A coterminal angle is an angle that ends at the same location as another angle. For example, 1 degree and 361 degrees are at the same location since the total angles in a circle are 360 degrees.

**What is the coterminal angle formula?**

The coterminal Angle can be calculated with one of the following:

Positive Coterminal Angle = Angle + 360

Negative Coterminal Angle = Angle -360